euctrl-pru/nvctr

R :package: about n-vector for geographical position calculations using an ellipsoidal model of Earth :globe_with_meridians:

nvctr

Overview

The nvctr package implements the n-vector approach to geographical position calculations using an ellipsoidal model of Earth as described in (Gade 2010).

Implementations in various computer languages can be found at the n-vector page (Navigation Group 2010).

Installation

You can install the development version of nvctr from GitHub with:

devtools::install_github("euctrl-pru/nvctr")

or the CRAN version (when this package will land to CRAN):

install.packages("nvctr")

Usage

nvctr can be used to solve geographical position calculation like (example numbers refer to the ones in the vignette):

• Calculate the surface distance between two geographical positions (Example 5).
• Find the destination point given start point, azimuth/bearing and distance (Example 8).
• Find the mean position (center/midpoint) of several geographical positions (Example 6).
• Find the intersection between two paths (Example 9).
• Find the cross track distance between a path and a position (Example 10).

References

Gade, Kenneth. 2010. “A Non-Singular Horizontal Position Representation.” Journal of Navigation. https://doi.org/10.1017/S0373463309990415.

Navigation Group, FFI. 2010. “The N-Vector Page.” https://www.navlab.net/nvector/.

nvctr's Issues

improve on EUROCONTROL logo

The current image for EUROCONTROL logo (from wikipedia) is the canonical one but it
could be beneficial to have one where the label is on the right of the logo:

EUROCONTROL

To be checked with Comms with regard to "Logo guidelines"

AppVeyor using tic

See past commit where tic version of AppVeyor was used: pandoc seemd to be the problem.
It would be nice to use tic for all.

n_E2lat_lon is incorrect for c(0, 0, 1)

It is smelly to have to add %% pi at L23 of n_E2lat_lon.
This is not in the original Matlab, so an even bigger suspicion of being wrong

create hex logo for the package

Maybe with https://github.com/GuangchuangYu/hexSticker

RE: How to benefit from bookdown features in pkgdown

If you are still interested in this question, I opened a pull request in pkgdown GitHub repo r-lib/pkgdown#1352 that addresses it.

add practical examples

From a request via email from Michael Henry from Australia about great circle intersection of
[point, bearing]_1 with [point, bearing]_2:

library(nvctr)
#> Warning: package 'nvctr' was built under R version 4.0.3

# find point on great circle at distance, from Example 8
point_at_distance <- function(n_EA_E, distance, azimuth, r_Earth = 6371e3) {
  k_east_E <- unit(pracma::cross(base::t(R_Ee()) %*%
                                   c(1, 0, 0) %>%
                                   as.vector(), n_EA_E))
  k_north_E <- pracma::cross(n_EA_E, k_east_E)
  d_E <- k_north_E * cos(azimuth) + k_east_E * sin(azimuth)
  n_EB_E <- n_EA_E * cos(distance / r_Earth) + d_E * sin(distance / r_Earth)
  n_E2lat_lon(n_EB_E)
}

# test 1
A <- c(-10, 0)
n_EA_E <- lat_lon2n_E(rad(A[1]), rad(A[2]))
azimuth <- rad(0)
s_AB <- 100000 # distance (m)
n_EB_E <- point_at_distance(n_EA_E, s_AB, azimuth)
(B <-  n_EB_E %>% deg()) # reassuringly longitude remains 0
#> [1] -9.100678  0.000000

# test 2
A <- c(0, -10)
n_EA_E <- lat_lon2n_E(rad(A[1]), rad(A[2]))
azimuth <- rad(90)
s_AB <- 100000 # distance (m)
n_EB_E <- point_at_distance(n_EA_E, s_AB, azimuth)
(B <-  n_EB_E %>% deg()) # reassuringly latitude remains 0 (well, close enough, 5.5e-17 !)
#> [1]  5.506349e-17 -9.100678e+00


# great circle intersection, from Example 9
great_circle_intersection <- function(n_EA1_E, n_EA2_E, n_EB1_E, n_EB2_E) {
  n_EC_E_tmp <- unit(pracma::cross(
    pracma::cross(n_EA1_E, n_EA2_E),
    pracma::cross(n_EB1_E, n_EB2_E)))
  n_EC_E <- sign(pracma::dot(n_EC_E_tmp, n_EA1_E)) * n_EC_E_tmp
  
  n_EC_E
}

# (too?) simple test
A1 <- c(-10, 0)
n_EA1_E <- lat_lon2n_E(rad(A1[1]), rad(A1[2]))
A2 <- c(10, 0)
n_EA2_E <- lat_lon2n_E(rad(A2[1]), rad(A2[2]))
B1 <- c(0, -10)
n_EB1_E <- lat_lon2n_E(rad(B1[1]), rad(B1[2]))
B2 <- c(0, 10)
n_EB2_E <- lat_lon2n_E(rad(B2[1]), rad(B2[2]))

n_EC_E <- great_circle_intersection(n_EA1_E, n_EA2_E, n_EB1_E, n_EB2_E)
(C <- n_E2lat_lon(n_EC_E) %>% deg()) # reassuringly gives (0, 0)
#> [1] 0 0

# ([less] too?) simple test
A1 <- c(-10, -10)
n_EA1_E <- lat_lon2n_E(rad(A1[1]), rad(A1[2]))
A2 <- c(10, 10)
n_EA2_E <- lat_lon2n_E(rad(A2[1]), rad(A2[2]))
B1 <- c(10, -10)
n_EB1_E <- lat_lon2n_E(rad(B1[1]), rad(B1[2]))
B2 <- c(-10, 10)
n_EB2_E <- lat_lon2n_E(rad(B2[1]), rad(B2[2]))

n_EC_E <- great_circle_intersection(n_EA1_E, n_EA2_E, n_EB1_E, n_EB2_E)
(C <- n_E2lat_lon(n_EC_E) %>% deg()) # reassuringly gives (0, 0)
#> [1] 0 0

^{Created on 2020-11-20 by the reprex package (v0.3.0)}

^{Created on 2020-11-20 by the reprex package (v0.3.0)}

^{Created on 2020-11-20 by the reprex package (v0.3.0)}

Exercise 10: find intersection

Exercise 10 needs to be completed with the position of the intersection on the great circle from A to B